Example 2.1.1.3. Let $M$ be a set, which we regard as a category having only identity morphisms. Then nonunital strict monoidal structures on $M$ (in the sense of Definitions 2.1.1.1) can be identified with nonunital monoid structures on $M$ (in the sense of Definition 2.1.0.3). In particular, any nonunital monoid can be regarded as a nonunital strict monoidal category (having only identity morphisms).

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$